Social justice in the mathematics classroom

DespiteincreasesineducationalattainmentinLondon,toomanymathematicslessonsremainfocusedonfactualrecallandproceduralunderstanding,resultingindisaffectionamonglearners.Thisstudyreportsontheestablishmentofaresearchgroup,comprisingfiveteacherresearchersandmyself,whichaimedtochallengethissituationthroughadoptingaparticipatoryactionresearchmethodology.Byplanning,teaching,andevaluatinginnovativeclassroomactivities,thegroupdemonstratedhowmakingmathematicsmorerelevantandmeaningfulcanenhance students’engagementandagency.Thecollaborativeandmutuallysupportivenatureofthe groupdevelopedteacherresearchers’self-efficacyinaddressingissuesofsocialjusticeintheirmathematicsclassrooms.


Introduction
You could be forgiven a degree of complacency towards the current state of mathematics educationinEnglandgivenapparentincreasesinattainmentoverthepast20years. Thepercentage of candidates achieving top grades (A* to C) in mathematics in the General Certificate of SecondaryEducation(GCSE)examination,takenattheendofcompulsoryschoolingatage16, hasrisensteadilyfrom45percentin1995to63percentin2015.ChildreninLondonschools outperformothersacrossEngland.Theabovemeasureofmathematicsperformanceiscurrently 2percenthigherinLondon,whichhasalsoseenasignificantlyhigherrateofimprovementin GCSEperformanceinrecentyearsthanelsewhere (GLA,2014).
Evidence suggests that teaching mathematics through more open-ended, collaborative, problem-solving approaches, with students in mixed-attainment groups, leads to more equitable outcomes and promotes greater participation among both boys and girls in postcompulsory mathematics education (Boaler, 2008). So why do conventional approaches to teachingmathematicspersistdespitethepriorityaffordedbygovernmentstowardsmathematics education over the past 30 years? Over the same period, consensus has grown among the mathematicseducationcommunitythatamorerelevantandengagingmathematicscurriculum isneeded,withgreateremphasisonconceptualunderstandingandproblemsolving (Cockcroft, 1982;ACME,2011;Ofsted,2012). Bourdieu(1998)arguesthatoneoftheprimaryfunctionsofschoolingistoreproducethe current social order and to maintain unequal power relations existing in society. It does this by concealing these relations, for example, by falsely attributing academic success to notions ofgiftednessormerit,whichisevidentintheprevalenceofsettinginmathematicsclassrooms. Schoolsclaimthattheyofferequalityofopportunity-whereas,inreality,somestudentspossess higher levels of the'cultural capital' that is recognized and valued by schools (Jorgensen et al., 2014). Bourdieu argues that, through their upbringing, children from middle-class families acquirehigherlevelsofculturalcapitalthanthosefromworking-classfamilies,placingthematan advantagebeforetheyarriveatschool (Noyes,2008).
Ioutlineinapreviouspaper (Wright,2012)howsuccessiveUKgovernmentshaveincreasingly intervenedinthedevelopmentoftheschoolcurriculum.Thishasledtoagreaterinfluenceon schoolmathematicsofeducationalideologiesthatchampiontheabstractandrigorousnature of the subject, and promote practices common in business and industry, including selection and marketization.This helps to explain why, despite government rhetoric calling for a new generation of creative and mathematically proficient problem-solvers able to drive forward economic growth, most students continue to experience mathematics lessons that involve completingaseriesofalmostidentical,closedquestions. Skovsmose(2011:9)describesthisasthe'exerciseparadigm',whichcultivatesa'prescription readiness' and 'prepares the students for participating in work processes where a careful following of step by step instructions without any question is essential'. Gutstein (2006: 10) argues that such a disempowering mathematics education for the majority reflects capitalist economies'needfor'anever-growingarmyoflow-skilled,compliant,docile,pleasant,obedient serviceworkers'.Aswellashelpingtounderstandandexplainthecurrentsituationdescribed above,suchcriticalperspectivesofferanalternativevisionofwhatmathematicseducationmight looklikeinpractice.
Practical organization involves cooperation between research participants in organizing an arranged situation.The second, fourth, and sixth meetings of the research group focused primarily on jointly planning activities to try out in the classroom.Teacher researchers were encouragedtopresentideastakenfromcurrentlyexistingresources (Wright,2004;Gutstein andPeterson,2005),discussinghowtheymightincorporatetheseintotheirlessons,bearingin mindtheconstraintsoftheclassroom.
Explorative reasoninginvolvesanalysingthearrangedsituationinordertobetterunderstand the current situation and the feasibility of the imagined situation.The third, fifth, and seventh meetingsoftheresearchgroupfocusedprimarilyonevaluatingandreflectingontheactivities tried out in the classroom.Teacher researchers took it in turns to present their evaluations, making use of student feedback, examples of students' work, and notes from their research journals to inform their presentations. Presentations were followed by questions from other teacherresearchersandageneraldiscussion,whichinformedsubsequentplanning,teaching,and evaluationcycles.
This thematic analysis made use of inductive coding, whereby the categories assigned to eachunitofmeaningwerederivedfrominitialreadingsofthedata.Categorieswerethenused to facilitate the comparison of commonalities, differences, and relationships between units of meaning, enabling new themes to emerge (Gibson and Brown, 2009). Such comparisons, in contrasttosimplisticcodingthatismoreeasilyquantified,takeintoaccountthecontextofthe text,allowingmeaningtobeconstructedfromthestoriesoftheresearchparticipants.Initial findingsfromthedataanalysiswerethenrelatedbacktothetheoriesunderlyingtheproject inordertogeneratenewanalyticalquestionsgivingfurthermeaningtothedata (Jacksonand Mazzei,2012).
Careful consideration was given to Lincoln and Guba's (2003) framework for ensuring the trustworthiness of qualitative research, with particular attention paid to the credibility, transferability,dependability,andconfirmabilityoftheresearchfindings.

Theme 2: Developing student agency
Threeoftheteacherresearcherscitedadesiretochangesocietyforthebetterasareason forbecomingamathematicsteacherinthefirstplace.Allfivesharedastrongbeliefintackling inequitythroughraisingtheattainmentofdisadvantagedstudents,whichexplainstheirchoiceof aninitialteachereducationprogrammethatplacedtheminschoolswithrelativelyhighlevelsof socioeconomicdeprivation.Theyviewedmotivatingstudentsasahighpriorityandconvincing students of the utility of mathematical procedures, by making the subject more realistic and meaningful,wasseenasawayofachievingthis.
IthinktheagencythingwasdefinitelysomethingIhadn'tconsideredatthestart.Like,Isawitmore asapplyingmathstodifferentsituations,ratherthanusingmathstoactuallychangesomething. (Rebecca,Interview3) The'Making a Change' project, which involved students using mathematics to develop their understanding of an issue of their choice and present an argument for a change they would liketoseemade,becamethefocusofthethirdactionresearchcycle.Whilefosteringstudents' mathematicalengagementandagencybecameincreasinglyimportanttotheteacherresearchers in the development of their practice, there was a growing appreciation that the notion of 'studentagency'neededtobehandledcarefully.Georgewarnedthatagency,onitsown,was notnecessarilydesirableasstudentsalsoneededtodevelopopen-mindednessandsensitivity towards issues of social justice in order to become positive agents of change.The question of whether teachers should encourage students to explore issues and arrive at their own conclusions,orguidestudentstowardsdevelopingparticularbeliefsandvalues,washighlighted duringtheFairtradeactivitywhensomestudentsopenlyquestionedthevalidityofFairtrade.
Ithinkmathstodaywasgoodasit'sshowingactualstatisticswhichhasmademethink'fairtrade' isn'tfair. (Year9studentinRebecca'sclassinresponsetoFairtradeactivity) The teacher researchers reported that most students responded positively to the activities, demonstratinggreaterlevelsofengagementandenjoymentoflearningthroughtheirbehaviour andresponsestothefeedbacksurvey.Thiswasparticularlynoticeableamongstudentswhohad previouslybeenpoorlymotivatedandbadlybehavedinmathematicslessons: I tried a few things with my bottom set and their motivation has just been so high in those particularlessonsthatI 'vehadtoveryrarely,like,tellthemtogetonwiththingsortodothings. (Anna,Interview3)  Thegroupquicklyestablishedpositiveworkingrelationships,helpedbythefactthattheyknew each other from their initial teacher education programme.The mutually supportive nature of the group encouraged the teacher researchers to take risks and overcome many of the challengesandconstraintstheyencounteredindevelopingalternativeclassroompractices: Andit'salsoprovidedthatadditionalincentivetodoit,andtotaketherisk,becauseyouknow thatyou'regoingtobeaskedtotalkaboutit.Butalsoyouknowyou'regoingtobeallowedto talkaboutitinawaythatsaysthatmessingupdoesn'tmatter. (Brian,Interview3) This was exemplified by the way in which the rest of the group encouraged and reassured RebeccaaftershepresentedtheevaluationofherinitialattemptattheMakingaChangeproject. Havingbeenthefirstinthegrouptotrytheactivity,shewasclearlydisheartenedbythelogistical problemssheencountered.However,therestofthegrouprecognizedthepotentialofherideas andwentontodevelopthemintoasuccessfulactivity.

Implications for mathematics teaching
The project demonstrated how mathematics can serve as a powerful means for developing students' understanding of issues of social justice, and that students are likely to develop an understandingofbothsocialjusticeissuesandmathematicalconceptswhenthereisameaningful linkbetweenthetwo.Itshowedhowstudentagencycanbedevelopedbyadoptingcollaborative, problem-solvingapproachestoteaching,andencouragingstudentstochoosewhichissuesto explore and which mathematical procedures to apply. Developing and presenting their own argumentsenablesstudentstogainanappreciationofhowmathematicscanbeusedtobetter understandasituationandtoargueforachange.
The project also demonstrated how engaging with research findings enables teachers to develop insight into structural inequities in mathematics education.Through developing an appreciationoftheprocessesthatleadsomestudentstobecomealienatedfrommathematics, teachersmaybecomemorewillingtousearangeofalternativepedagogieswithstudentswho arelesspredisposedtowards,buthavethemosttogainfrom,discursive,open-endedapproaches tolearning.
Anotherissuehighlightedbytheprojectwashowuncommonitisforstudents,eventhose studyingmathematicsatdegreelevel,tobeaskedtoreflectonthenatureofthesubjectdespite the privileged position it occupies in the school curriculum. Encouraging students to do so appearstobeaneffectivewayofchallengingmyths,suchasthebeliefthatmathematicsisvaluefreeorthatmathematicalsuccessispre-determinedbyinnateability,perhapspreventingthese myths from being perpetuated from one generation to the next. Enabling students to better understandtheirownsituationcanhelpthosewhoaredisadvantagedinlearningmathematics toovercomebarrierstoachievingsuccess.Furthermore,theprojectemphasizedtheimportance ofestablishingrelationshipsbasedontrustandmutualrespectbetweenteacherandstudentsif suchdiscussionsaretohaveanyeffect.

Implications for the professional development of mathematics teachers
Theprojectdemonstratedhowthecriticalresearchmodel,withitsfocusonrelatingtheoryto practiceandensuringthatthecurrentsituationisnottakenasgiven,canhaveaconsiderable impact on the thinking and classroom practice of mathematics teachers with a concern for socialjustice.Theroleoftheexternalpartner-infacilitatingtheengagementofsuchteachers withresearchfindings,andencouragingthemtocriticallyappraisetheirownpracticeinrelation to theory -was shown to be a crucial aspect of the model.This process allows teachers to developamoreprofoundandcriticalunderstandingoftheirownpracticeandhowthisrelates toexistingpracticeacrossdifferentschools.Itcanleadtogreaterawarenessofstructuralcauses ofinequityandinjusticeinmathematicseducation,includingtheuseofsettingtogroupstudents byattainmentandignoringtheeffectofsocialclassonstudents'achievement.
The project highlighted the effectiveness of a collaborative, participatory, and sustained approachtoprofessionaldevelopment.Collaborativerelationshipsthatdevelopoveraprolonged periodoftimeenableteacherstoprovidethemutualsupportnecessarytoovercomeconstraints and to take risks in the classroom.Through the joint planning of lessons and the sharing of experiencesamongcolleaguesfromarangeofdifferentschools,teachersareabletoengagewith newideasanddeveloptheirthinkingappreciably.Thecriticalresearchmodeldemonstrateshow teachersareabletodeveloptheiragencyandself-efficacyindecidingthedirectionandextent ofchangesintheirclassroompractice.

Implications for mathematics education research
The project demonstrated how the critical research model can enable teachers, through reflecting on classroom practice and its underlying theories, to generate relevant knowledge thatistransferabletootherclassroomsituations.Theprojectshowedhowresearchundertaken collaborativelywithteachersworkingin'typical'classroomsituations(i.e.thosewherecommon issuesandconstraintsrelatingtodevelopingpracticearepresent)islikelytobeperceivedas relevantandauthenticbyotherteachers.Suchresearchthereforehasthepotentialtoincrease teachers'engagementwithresearchfindings.
The critical aspect of the research design enables new knowledge to be generated that challengesexistingdiscoursesinschools,andhasthepotentialtoaddressinequitiesandinjustices existing within mathematics classrooms, schools, and wider society. The project outlined processesthatenabletransformationsinclassroompracticetotakeplace,andhighlightedhow university-basedresearchersandteacherresearcherscanactcollaborativelyasagentsofchange.
Research based on collaborative and participatory methodologies is generally underrepresented in academic journals, reflecting a lack of confidence in its reliability.Through the attentionpaidtoissuesoftrustworthiness,onlysomeofwhichispresentedinthispaper,the project demonstrated how participatory action research from a critical perspective can be systematicandrigorous,aswellasgeneratingrelevantknowledgewiththepotentialtobring aboutpositivesocialchange.

Conclusion
The research project reported in this paper provides some insight into what teaching mathematicsforsocialjusticemightlooklikeinpractice,andhowitcanbepromotedthroughan effectivemodelofprofessionaldevelopment.Italsodemonstrateshowteachersandresearchers canworkcollaboratively,throughsystematicinquiry,whichgeneratesreliableandtrustworthy findings,tochallengethecurrentsituationinwhichmathematicsteachingperpetuatesinequities and injustices within society. It is unlikely that those in positions of power will embrace the findingsofthisresearch,sincetheirinterestsmightbebetterservedbymaintainingthestatus quo.However,itishopedthatthosecommittedtoeducationasameansofchangingtheworld forthebettermightgainsomeinsightfromtheproject'sfindingsintohowtogoaboutbringing aboutpositivechangeinthemathematicsclassroom.